THE ANALYTIC SOLUTION OF INITIAL BOUNDARY VALUE PROBLEM INCLUDING TIME FRACTIONAL DIFFUSION EQUATION


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Çetinkaya S. , Demir A. , Kodal Sevindir H.

FACTA UNIVERSITATIS-SERIES MATHEMATICS AND INFORMATICS, vol.35, no.1, pp.243-252, 2020 (Journal Indexed in ESCI) identifier

  • Publication Type: Article / Article
  • Volume: 35 Issue: 1
  • Publication Date: 2020
  • Doi Number: 10.22190/fumi2001243c
  • Title of Journal : FACTA UNIVERSITATIS-SERIES MATHEMATICS AND INFORMATICS
  • Page Numbers: pp.243-252
  • Keywords: Caputo fractional derivative, space-fractional diffusion equation, Mittag-Leffler function, initial-boundary-value problems, spectral method, PARTIAL-DIFFERENTIAL-EQUATIONS

Abstract

The motivation of this study is to determine the analytic solution of initial boundary value problem including time fractional differential equation with Neumann boundary conditions in one dimension. By making use of seperation of variables, the solution is constructed in the form of a Fourier series with respect to the eigenfunctions of a corresponding Sturm-Liouville eigenvalue problem.